Western civilization in Antiquity forms a continuous society with different state organizations stretching from the time of Homer and Hesiod in Greece (c. 800 BCE) through the fall of the western Roman Empire, often dated as 476 CE, a period considerably longer than a millennium. The main societies, usually termed Greek and Roman, could more properly be termed Greek speaking and Latin speaking, although Greek includes several dialects, such as Ionian and Attic, Doric, Macedonian (perhaps not even Greek), and koine, the common Greek of later times. The period is called Classic with regard to its literature and philosophy.
Although Ionian, Greek, and Hellenic science was of the highest order found in ancient times –– the Ionians of the seventh century BCE virtually invented science –– there were few technological advances. The beam wine/olive press comes to mind as the most characteristic mechanical invention, although there were a few others. The Romans had neither a distinguished scientific tradition nor an adventurous technology. Known engineering principles were often exploited more completely than in the past, as in Roman roads and aqueducts.
By far the most advanced technology invented under Roman rule outside of Hellenic centers was the water wheel, but it was not exploited systematically until after the fall of the Western Empire. During this entire period virtually all significant advances in technology were made in China and apparently not communicated to the Romans despite steady trade with the Chinese in various goods. As many theories have been advanced as to why there are so few classical machines as there are reasons put forward for the fall of the Roman Empire or the demise of the dinosaurs. Unlike the extinction of dinosaurs, whose cause is now becoming clear, the true explanation of the empire’s fall or its technological stasis will probably never be known.
The later inventors of Antiquity had sufficient means to produce machinery as advanced in concept as that of the early Industrial Revolution. In particular, the somewhat shadowy Heron of Alexandria, probably about the first century CE, described devices that included all the elements needed to build a functional and useful steam engine, either turbine or piston driven. But he used these devices as either toys or as machines priests could install in temples to make it seem that small miracles were taking place. He did not employ them as practical pumps (the first use for piston steam engines in the 18th century) or to power mills or move vehicles. In the 1670s, before truly practical steam engines, Ferdinand Verbiest made a version of Heron’s steam turbine (aeolipile). He installed it in a cart and promptly drove the cart a few inches with it. With that in mind, we can boil down the question of why there are no machines to speak of in Antiquity to the even more specific one of why the later Greeks or Romans did not use steam power. The common reasons put forward include the following:
Slavery: Greek and Roman upper classes had an ample supply of barbarian slaves, so they not only did not need steam power, but they also equated anything related to work as definitely lower class and to be avoided.
Poor natural resources: The Mediterranean region does not contain large deposits of either coal or iron ore. Indeed, when Marco Polo reported that people in China burned black rocks as fuel, Italians thought he was making things up.
Lack of scientific background: Science and technology evolve, just as organisms do. You could no more expect a steam engine before the invention of the thermometer, the microscope, and so forth than you could expect flowering plants before algae, mosses, and ferns.
Lack of technical background: Gear-cutting and screw cutting machines were not devised until the 15th and 16th centuries, when they were used by clock makers. Without metal lathes and similar devices, even the best designed machine would have been impossible to build well enough to function.
Greeks and Romans had other things on their mind: There was a great religious movement for hundreds of years in Hellenic and Roman times, the most likely times for progress on steam engines. People did not care about the material world, only the spiritual one. Evidence for this is that the cleverest devices of the period were devoted to causing temple doors to open mysteriously or to produce other apparently miraculous effects.